Background: Planck's theory of radiation
In late 19th century, Max Planck was working on a theory of black body radiation, and ran into two problems:
where E is the energy of the `quantum', 
is the frequency of radiation, and h is a fundamental constant.
The constant, later known as Planck's constant, has significance beyond
the model of black body radiation, and is a major building block of Quantum
Mechanics and Quantum Field Theory.
The Photoelectric Effect and Einstein's explanation
Photoelectric emission is a process in which light strikes a surface of material (e.g. a metal), and electrons come out. The kinetic energy of these electrons can be measured by subjecting them to a retarding electric field. The maximal kinetic energy is obtained when the electric field is strong enough to overcome all electrons.
In early 1900s, several experiments showed that:
Einstein took Planck's theory one step further and in 1905 stated that
in the photoelectric process a photon of energy
is absorbed by electrons that are assumed to be bound within the surface
of material with some energy 
.
The energy of the photon is used by the electron to escape the atom and
the the rest is electron's kinetic energy 
.
This is summed up in Einstein's famous equation:
If a retarding potential V is used to stop electrons,
that will happen when eV =.
(Note that in truth a third term exists - the kinetic energy of the recoiling
material necessary to ballance the electron's momentum, but it's neglected
as infinitely small.) When solved for stopping potential V,
this turns into
so if we plot V as a function of frequency ,
we should get a linear dependence with a slope equal to h/e!
Here /e
is called
work function and is a propety of the material.
This model thus makes a very definite prediction as to what the dependence
of V on
ought to be. The goal of this experiment is to verify it, and, if
true, to use it to measure h/e.
Notes
Max Planck was awarded the Nobel Prize in 1918 for his quantum theory.
Albert Einstein got his in 1921 - for the explanation of the photoelectric
effect. Robert Millikan felt very strongly that Einstein's explanation
was wrong, and worked very hard for many years to perform ever more precise
measurements of photoelectric effect. In the end he failed, confirming
the quantum explanation. But he got a Nobel Prize as a consolation.
The Experiment
Experimentally, we need a clean surface of a metal which will be exposed to light and yield electrons, and therefore called cathode below. We also need another surface to collect electrons - an anode - facing the cathode, and both are sealed in vacuum. We shine light of different intensities and frequencies (colors) onto the cathode, and it emits electrons that are collected on the anode. (The stream of electrons forms so-called photoelectric current.)
As a source of monochromatic light it is customary to use a mercury
bulb. The most readily available lines are:
| Color | Frequency [10^14 Hz] | Wavelength [nm] |
| Yellow | 5.18672 | 578 |
| Green | 5.48996 | 546.074 |
| Blue-green (weak) | 6.09830 | 491.6 |
| Blue | 6.87858 | 435.835 |
| Violet | 7.40858 | 404.656 |
| Ultraviolet | 8.20264 | 365.483 |
The values for green, blue, violet and ultraviolet are copied from PASCO manual which quotes "Handbook of Chemistry and Physics", 46th ed. The wavelength for Yellow was determined experimentally by PASCO using a grating with 600 lines/mm. The line is a doublet at 578 and 589 nm. The value for blue-green was copied from Melissinos.
Although invisible, the ultraviolet light can be seen on the white reflective
mask of the h/e apparatus, which is made of a special
fluorescent material. Ultraviolet line
will appear as blue. The violet will also appear bluish.
Using the filters
The h/e apparatus (PASCO AP-9368) includes three filters:
Green and Yellow filter block the higher frequencies, which prevents the ambient room light from interfering with the lower frequency green and yellow lines from the mercury spectrum. These filters must be used when working with green and yellow spectral lines.
The variable transmission filter does not affect the frequency of the
incident light, but only its intensity. There are five slots for
the input light with transmission percentages of 100%, 80%, 60%,
40% and 20% respectively. (As an aside, this filter actually consists
of fine patterns of dots and lines generated by a computer.)
Measuring stopping voltage: classical approach
Experimentally, the most challenging part is to have a precise measurement
of the stopping voltage. In the past, the measurement of voltage
was usually turned into the measurement of a very small current running
through a high-resistance circuit. This approach introduces a couple
of difficulties, the most important being that now the anode and the cathode
are coupled through an external circuit, and one must
also take into account the `contact potential difference', which
is in fact equal to the difference of work functions between the cathode
and the anode! Thus
the work function of the anode is dragged into the calculation and has
to be measured separately.
Measuring stopping voltage: with PASCO AP-9368
In contrast to the traditional approach, the PASCO setup uses
the photoelectric current itself to charge the anode and create the retarding
potential! The photoelectric current will stop when the stopping
potential is reached, and at that time the voltage between the anode and
the cathode will equal the stopping voltage, V. All
this is possible if the measurement of V does not leak any
charge from the anode, and PASCO AP-9368 contains an built-in operational
amplifier with an
ultra-high impedance (> 
)
and unity gain, which is directly connected to the output jacks.
This ellegant approach circumvents the problems present in the `classical' setup of the photoelectric experiment. However, it has two operational consequences:
